Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order

Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order

We study, in this paper, the Cauchy problem for matrix factorizations of the Helmholtz equation in the space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-stru...

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Bibliographic Details
Main Authors: Davron Aslonqulovich Juraev, Ali Shokri, Daniela Marian
Format: Article
Language:English
Published: MDPI AG 2022-06-01
Series:Fractal and Fractional
Subjects:
Carleman matrix
stability of the Cauchy problem
regularized solution
approximate solution
Online Access:https://www.mdpi.com/2504-3110/6/7/358
Description
Summary:We study, in this paper, the Cauchy problem for matrix factorizations of the Helmholtz equation in the space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>m</mi></msup></semantics></math></inline-formula>. Based on the constructed Carleman matrix, we find an explicit form of the approximate solution of this problem and prove the stability of the solutions.
ISSN:2504-3110

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